Solve for $x$ and $y$ using elimination. ${-3x-2y = -25}$ ${-x-5y = -43}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-3$ ${-3x-2y = -25}$ $3x+15y = 129$ Add the top and bottom equations together. $13y = 104$ $\dfrac{13y}{{13}} = \dfrac{104}{{13}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {-3x-2y = -25}\thinspace$ to find $x$ ${-3x - 2}{(8)}{= -25}$ $-3x-16 = -25$ $-3x-16{+16} = -25{+16}$ $-3x = -9$ $\dfrac{-3x}{{-3}} = \dfrac{-9}{{-3}}$ ${x = 3}$ You can also plug ${y = 8}$ into $\thinspace {-x-5y = -43}\thinspace$ and get the same answer for $x$ : ${-x - 5}{(8)}{= -43}$ ${x = 3}$